A critical Galton-Watson branching process Z(n)in a random
environment e(n) ,n=0,1,... is considered. Assuming that {e(n)} is
an irreducible aperiodic positive recurrent Markov chain we prove,
as n tends to infinity a Yaglom-type conditional functional limit
theorem for the suitably normalized process {Z(nt),0<t<1} given
Z(n)>0. The statement we have proved generalizes several known
results for the critical branching processes in random environment
generated by a sequence of independent identically distributed
random variables.

branching processes; random environment